OPE中的重整子鞍点
Renormalon Saddles in the OPE
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中文总结 AI 辅助
本文在大N Gross--Neveu模型中赋予重整子不确定性消除以等值线实现，识别重整子鞍点为边界临界点，并证明微扰系数与重整化凝聚构成互补相对环。
中文摘要 AI 辅助
算符乘积展开中重整子不确定性的消除通常被表述为微扰Borel不确定性与非微扰凝聚项中处方依赖性之间的匹配。我们在二维Gross--Neveu模型的大$N$极限下赋予这种消除以等值线实现。大质量真空中的精确$1/N$阶费米子自能是一个有限的实积分；只有当其大动量行为被分解为微扰Wilson系数与相关算符矩阵元的乘积时，不确定性才会出现。一个约化积分分离出领头重整子，并揭示了一个二维等值线几何结构，其中微扰级数在边界角点产生，该角点处交换动量达到外部硬标度，而其Stokes不连续性则由零交换动量处的一个不同边界临界点控制。在对凝聚标度积分的紫外发散进行重整化后，我们推导出其补偿的横向不确定性，而无需通过匹配微扰部分来固定它，区分了重整子鞍点与表观红外Landau极点，并从大$N$辅助场路径积分中获得约化等值线变量。重整子鞍点是该约化模空间积分的边界临界点。因此，微扰Wilson系数和重整化凝聚定义了同一约化被积函数的互补相对环，其复数尾部相互抵消，重构了原始实积分环。
英文摘要
The cancellation of renormalon ambiguities in the operator product expansion is usually formulated as a matching between perturbative Borel ambiguities and prescription dependence in non-perturbative condensates. We give this cancellation a contour realization in the two-dimensional Gross--Neveu model at large $N$. The exact order-$1/N$ fermion self-energy in the massive vacuum is a finite real integral; ambiguities arise only after its large-momentum behavior is decomposed into products of perturbative Wilson coefficients and the matrix elements of the associated operators. A reduced integral isolates the leading renormalon and reveals a two-dimensional contour geometry in which the perturbative series is generated at the boundary corner where the exchanged momentum reaches the external hard scale, while its Stokes discontinuity is controlled by a distinct boundary critical point at zero exchanged momentum. After renormalizing the ultraviolet divergences of the condensate scale integral, we derive its compensating lateral ambiguity without fixing it by matching to the perturbative sector, distinguish the renormalon saddle from the apparent IR Landau pole, and obtain the reduced contour variables from the large-$N$ auxiliary-field path integral. The renormalon saddle is a boundary critical point of this reduced mode-space integral. The perturbative Wilson coefficient and the renormalized condensate thus define complementary relative cycles of the same reduced integrand whose complex tails cancel, reconstructing the original real integration cycle.
发表机构
- Deutsches Elektronen-Synchrotron DESY（德国电子同步加速器）
- Department of Physics, Harvard University（哈佛大学物理系）
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